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A solid cone of height $180 \mathrm{mm}$ with a circular base of radius $60 \mathrm{mm}$ is supported by a ball and socket at $A .$ The cone is released from the position $\theta_{0}=30^{\circ}$ with a rate of $\operatorname{spin} \dot{\psi}_{0}=300 \mathrm{rad} / \mathrm{s},$ a rate of precession $\dot{\phi}_{0}=20 \mathrm{rad} / \mathrm{s},$ and a zero rate of nutation. Determine (a) the maximum value of $\theta$ in the ensuing motion, ( $b$ ) the corresponding values of the rates of spin and precession. (Hint: Use Eq. (2) of Prob. $18.138 ;$ you can either solve this equation numerically or reduce it to a quadratic equation, given that one of its roots is known.

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Physics 101 Mechanics

Chapter 18

Kinetics of Rigid Bodies in Three Dimensions

Section 3

Motion of a Gyroscope

Rotation of Rigid Bodies

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Lectures

02:34

In physics, a rigid body is an object that is not deformed by the stress of external forces. The term "rigid body" is used in the context of classical mechanics, where it refers to a body that has no degrees of freedom and is completely described by its position and the forces applied to it. A rigid body is a special case of a solid body, and is one type of spatial body. The term "rigid body" is also used in the context of continuum mechanics, where it refers to a solid body that is deformed by external forces, but does not change in volume. In continuum mechanics, a rigid body is a continuous body that has no internal degrees of freedom. The term "rigid body" is also used in the context of quantum mechanics, where it refers to a body that cannot be squeezed into a smaller volume without changing its shape.

06:08

The angular velocity of a rigid body is the rate of change of the angular displacement relative to time. In SI units, it is measured in radians per second.

02:24

The solid cone of mass $m$…

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